A256654 Least Fibonacci number not less than n.

1, 2, 3, 5, 5, 8, 8, 8, 13, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89

Offset

1,2

Comments

This sequence plays a role in the definition of minimal alternating Fibonacci representations, introduced at A256655.

Essentially the same as A246104. - R. J. Mathar, Apr 14 2015

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Formula

Concatenate these numbers: F(2), F(3), F(4), then F(3) F(5)'s, then F(4) F(6)'s, then F(5) F(7)'s, ... F(n+2) F(n)'s, ..., where F = A000045, the Fibonacci numbers.

Sum_{n>=1} 1/a(n)^2 = 1 + Sum_{n>=1} F(n)/F(n+2)^2 = 1.5651369873... . - Amiram Eldar, Aug 16 2022

Mathematica

h[0] = {1}; h[n_] := Join[h[n - 1], Table[Fibonacci[n + 2], {k, 1, Fibonacci[n]}]]; h[10]

Crossrefs

Cf. A000045, A087172, A246104, A256655.

Sequence in context: A353272 A123339 A246104 * A204926 A256663 A188201

Adjacent sequences: A256651 A256652 A256653 * A256655 A256656 A256657

Keyword

nonn,easy

Author

Clark Kimberling, Apr 08 2015

Status

approved